PSY201: Chapter 7 - Sample Means

Question 1

Samples and Populations

Answer 1

can choose 1000s of potential samples from pop - have to worry about sampling error
diff samples will differ from each other ⇒ won’t necessarily have same sample means

Question 2

Distribution of Sample Means

Answer 2

set of possible samples forms pattern⇒ distribution of sample means - allows us to predict sample characteristics
set of sample means for all the possible random samples of specific size (n) that can be selected from a pop

Question 3

Distribution of Sample Means

Answer 3

we need to make inferences about sample mean rather than single score
distribution of sample means is diff from distribution of scores because sample means are statistics ⇒ sampling distribution

Question 4

Distribution of Sample Means

Answer 4

statistic obtained by selecting all possible samples of specific size from a pop
sample means pile up around pop mean because they are representative of pop

Question 5

Distribution of Sample Means

Answer 5

pile of sample means tends to be normally distributed
rare to find sample means really far from μ
larger the sample size⇒ closer sample means typically are to μ

Question 6

Distribution of Sample Means

Answer 6

very important distribution

spread of sampling distribution of mean decreases as sample size increases

Question 7

Distribution of Sample Means

Answer 7

mean of the distribution is not affected by sample size

Question 8

The Central Limit Theorem

Answer 8

distribution of sample means has well-defined, predictable characteristics specified in the Central Limit Theorem:
Given distribution with a mean μ + standard deviation σ

Question 9

The Central Limit Theorem

Answer 9

sampling distribution of the mean approaches normal distribution with a mean of μ + standard deviation of σ/√n, as n approaches infinity
n = sample size
# of samples assumed to be infinite.

Question 10

The Central Limit Theorem

Answer 10

Sample mean distributions approach a normal distribution very quickly as n increases, even if original distribution is not normal

Question 11

The Central Limit Theorem

Answer 11

assume sample mean distribution is normal if either:
pop from which samples are obtained is normal
sample size is n>/=30

Question 12

The Central Limit Theorem

Answer 12

expect sample means to be close to pop mean
sample means should “pile up” around μ
distribution of sample means tends to form a normal shape

Question 13

The Central Limit Theorem

Answer 13

mean of distribution of sample means = Expected Value of M

always = μ

Question 14

The Central Limit Theorem

Answer 14

individual sample mean will probably not be identical to its pop mean; some error between M and μ.
Some sample means relatively close to μ, others will be relatively far away

Question 15

The Central Limit Theorem

Answer 15

standard distance between M and μ = Standard Error of M

standard deviation of distribution

Question 16

The Central Limit Theorem

Answer 16

standard error of M measures how well sample mean represents entire distribution
σ2M = σ2/n
SEM=σM = σ/√n

Question 17

Standard Error

Answer 17

describes distribution of sample means

how much difference is expected from 1 sample to another

Question 18

Standard Error

Answer 18

measures how well individual sample mean represents entire distribution
how much distance is reasonable to expect betw a sample mean + pop mean for distribution of sample means

Question 19

Standard Error

Answer 19

population standard deviation, σ measures standard distance betw a single score (X) + population mean.
standard deviation provides a measure of the error expected for smallest possible sample, when n = 1

Question 20

Standard Error

Answer 20

As the sample size increases, ⇒ error should decrease

larger the sample, more accurately should represent its population

Question 21

law of large numbers

Answer 21

larger the sample size, n, more probable it is sample mean will be close to pop mean.

Question 22

Standard Error

Answer 22

Determined by sample size
Determined by standard deviation of pop
if you have a lot of variability in pop ⇒ higher SEM

Question 23

z-score

Answer 23

can be computed for each sample mean
tells where specific sample mean located relative to all other sample means
must remember to consider the sample size (n) + compute SE before you start any other computations

Question 24

Probability and the Distribution of Sample Means

Answer 24

distribution of sample means must satisfy at least 1 of criteria for having normal shape before you can use unit normal table

Question 25

Probability and the Distribution of Sample Means

Answer 25

normal sample mean distribution ⇒ can describe how particular sample related to another potential sample
an look up probabilities in unit normal table regarding likelihood of particular sample given makeup of pop

Question 26

Probability and the Distribution of Sample Means

Answer 26

probability associated with specific sample mean = proportion of all possible sample means

Question 27

Probability and the Distribution of Sample Means

Answer 27

z = M−μ/σM

Question 28

Probability and the Distribution of Sample Means

Answer 28

positive z-score = M > μ + negative z-score = M < μ

numerical value of the z- score indicates distance betw M + μ in terms of standard error

Question 29

Probability and the Distribution of Sample Means

Answer 29

procedure for finding probabilities for sample means is same as we used for individual scores

Question 30

Looking Ahead to Inferential Statistics

Answer 30

there is always margin of error that we must consider when we use sample mean to make inferences about pop mean.

Question 31

Looking Ahead to Inferential Statistics

Answer 31

Determine whether manipulated independent variable had effect on our dependent variable - sample mean for treatment group really different from sample mean for the control group
use distribution of sample means + standard error to help us make this decision

Question 32

Looking Ahead to Inferential Statistics

Answer 32

use the distribution of sample means to show what we would expect scores to be for a control group
If treatment group is not noticeably different from expected mean distribution scores⇒ treatment did not have an effect

Question 33

Looking Ahead to Inferential Statistics

Answer 33

use criteria of there being z = +/- 1.96

Question 34

Looking Ahead to Inferential Statistics

Answer 34

standard error tells us how close diff sample means are clustered around true pop mean
small SE ⇒ most samples similar, doesn’t really matter which sample we get

Question 35

Looking Ahead to Inferential Statistics

Answer 35

SE large ⇒ lot of deviation from sample to sample, sample might not be representative
we will want to replicate our results using diff samples to become more confident in findings
simple solution: obtain as large a sample as we can
remember: SE gets smaller when we increase n